WAVE EQUATIONS WITH LOGARITHMIC NONLINEARITY ON HYPERBOLIC SPACES

被引：0
作者：
Wang, Chengbo [1 ]
Zhang, Xiaoran [2 ,3 ]
机构：
[1] Zhejiang Normal Univ, Sch Math Sci, Jinhua 321004, Peoples R China
[2] Zhejiang Univ, Sch Math Sci, Hangzhou 310058, Peoples R China
[3] Beijing Inst Math Sci & Applicat, Beijing 101408, Peoples R China
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2025年
关键词：
Strauss conjecture; shifted wave; hyperbolic spaces; logarithmic nonlinearity; GLOBAL EXISTENCE; BLOW-UP;
D O I：
10.1090/tran/9404
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In light of the exponential decay of solutions of linear wave equations on hyperbolic spaces H-n, to illustrate the critical nature, we investigate nonlinear wave equations with logarithmic nonlinearity, which behaves like (ln 1/|u|)(1-p) |u| near u = 0, on hyperbolic spaces. Concerning the global existence vs blow-up with small data, we expect that the problem admits a critical power p(c)(n) > 1. When n = 3, we prove that the critical power is 3, by proving global existence for p > 3, as well as generically blow-up for p is an element of (1, 3).
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收藏
页码：2253 / 2269
页数：17
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